Pearling Bifurcations in the strong Functionalized Cahn-Hilliard Free Energy

TL;DR

This paper analyzes the stability of phase-separated morphologies in the Functionalized Cahn-Hilliard model, revealing how pearling bifurcations depend on parameters but not on surface shape.

Contribution

It characterizes the linear stability of bilayer and filament morphologies and identifies the parameters controlling pearling bifurcations in the strong functionalization regime.

Findings

Pearling onset depends on functionalization parameters and chemical potential.

Pearling bifurcation is shape-independent.

The study advances understanding of morphological stability in phase separation models.

Abstract

The Functionalized Cahn-Hilliard free energy supports phase separated morphologies of distinct codimension, including codimension-one bilayer and codimension-two filament morphologies. We characterize the linear stability of bilayer and filament morphologies associated to hypersurfaces within the strong functionalization scaling. In particular we show that the onset of the pearling instability, which triggers fast in-plane oscillations associated to bifurcation to higher codimensional morphology, is controlled by the functionalization parameters and the spatially constant value of the far-field chemical potential. Crucially, we show that onset of pearling is independent of the shape of the defining hypersurface.